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# Lumped elements to distributed elements

#### rf997

##### Junior Member level 2
Hello, I want to design a notch filter at 3.7 ghz frequency. When I design the circuit with lumped elements, some capacitor and inductor values are too small. So I want to replace these elements with microstrip lines. How can I do that?

Microstrip is a good option for low capacitance with a low-loss tangent dielectric on 1 side and air on the other side.

For a rule of thumb with Zo=sqrt(L^2/C^2) strips have an incremental Lo and Co per mm that determine Zo.
e.g. if Er=4 @ 3.7 GHz and if the track width, W to height, H above gnd W/H=2:1 then Zo ~ 50 Ohms. But the tolerance Er can be higher than your error tolerance requirements, so electrical testing is an added cost, or there are trimming methods. Here, Co is ~1.14 pF/cm and Lo is ~2.93 nH/cm. So choice of dielectric is key to the design. Getek FR4 is one brand that is popular for low loss at a reasonable cost.

Spiral inductors save space and vias also have L, C properties based on geometric ratios.

There are many good references online.

https://www.mdpi.com/2079-9292/8/9/964/htm

Use Microstrip Lines.A sample for you..

Thank you very much. but I have a few questions. How did you calculate the lengths of the resonators? Also, what are the total length and width of the filter in this design?
There are tons of information on internet.

How did you calculate the lengths of the resonators?
Do you know the impedance of an open ended lambda/4 stub?
Can you imagine what that does if connect it to a thru line?

The layout shown by BigBoss looks like a refined version with couplers instead of direct connection to the thru line.

The simplest microstrip notch it use an L-shaped coupled structure (as was shown above).
But the preferred one is using an U-shaped coupled structure, which gives the advantage of lower out of band insertion loss and higher notch rejection.
Adding more coupled U-elements to the line, improve the notch rejection.

Better results on Rogers Duroid 5880. If you want, I can post DXF or Gerber File here.

I will be very happy if you send it.
DXF File and Sonnet Archived/Packed file to whom might interested in.

#### Attachments

• 3.7GHz_notch_filter.rar
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• sonfile.rar
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Thanks for your help. However, my teacher asked me to first build the circuit with lumped elements and then replace the low values with stubs using the equations in the link. However, when I use these equations, I can not get results. Now I built the circuit with microstrip but it repeats in the frequency spectrum. Can I solve this problem by adding lumped element?

Thanks for your help. However, my teacher asked me to first build the circuit with lumped elements and then replace the low values with stubs using the equations in the link. However, when I use these equations, I can not get results. Now I built the circuit with microstrip but it repeats in the frequency spectrum. Can I solve this problem by adding lumped element?

You're using FR-4 substrate and this materiel is very lossy at 5.8GHz.
Also, transforming lumped components onto distributed elements won't work in all cases. Therefore special filter structures have been developed by engineers and scientists.
Try to use less lossy substrate and optimize the distributed elements' dimensions. You'll get a reasonable result but this will be worse in practical measurements.

Now I built the circuit with microstrip but it repeats in the frequency spectrum. Can I solve this problem by adding lumped element?
A transmission line band stop will typically have additional notches at odd multiples of the center frequency. Notches below threefold frequency suggest unsuitable topology, however what's your specification? You didn't talk about frequency range before.

A transmission line band stop will typically have additional notches at odd multiples of the center frequency. Notches below threefold frequency suggest unsuitable topology, however what's your specification? You didn't talk about frequency range before.

I'm trying to make a notch filter with a bandwidth of 200 Mhz at a center frequency of 3.7 GHz operating between 1.5-6.5 GHz. That's why it shouldn't repeat itself between 1.5-6.5 GHz.

You're using FR-4 substrate and this materiel is very lossy at 5.8GHz.
Also, transforming lumped components onto distributed elements won't work in all cases. Therefore special filter structures have been developed by engineers and scientists.
Try to use less lossy substrate and optimize the distributed elements' dimensions. You'll get a reasonable result but this will be worse in practical measurements.
Hello, is there a way to increase the bandwidth of the l resonator circuit, of which you sent the dxf file above, to 200 Mhz?

Perhaps, if you can realize something like these with exceptionally low L & C in rigid geometry stripline surface waves.

0.1 pF was rounded up from 0.05 pF

Some properties seem impossible at first glance to realize with L/C and L*C effects in Transverse or Longitudinal (surface) wave effects over such a wide range fmax/min (>2:1) in such small values.
--- Updated ---

Over a smaller frequency range might look like this.

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Hello, is there a way to increase the bandwidth of the l resonator circuit, of which you sent the dxf file above, to 200 Mhz?
-Pass Bandwidth
-Stop Bandwidth
-Stop Bandwidth Attenuation

-Pass Bandwidth
-Stop Bandwidth
-Stop Bandwidth Attenuation
3600-3800 MHz S21 is under -15dB,
S11 is under -30dB among 1500-6500 Mhz except stopband